You can create a normal Minecraft server, then remove all the files from the public folder and copy over your current server files over inside of the public folder, you will have to fix 2 things before you start it however...

Files will not being owned by the server user so it can't write to them. To fix this, you need to get username for the server, it will look something like "pp-testb_cw1awwi" if you named the server "testbox". Run this command as root or with sudo replacing <username> with the servers username

chown -R <username>:<username> /home/<username>/public

Pufferpanel will execute "server.jar" on startup. You will need to rename your main jar this.

Let me know if you have questions about my answer, this is my first reply :P
-piajesse